Timeline for Almost $p$-Kahler metric
Current License: CC BY-SA 3.0
11 events
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| Dec 25, 2011 at 15:13 | comment | added | Robert Bryant | @y2011: I cleaned up the question text a bit. Let me know if I mangled your meaning. Assuming that I've understood you correctly, I'll just comment that, without imposing some kind of positivity(?) condition on $\sigma$, you are not likely to get anything interesting because $\omega$ essentially washes out without some restriction. As diverietti remarked, taking $\sigma=-\omega^p$ will make any metric satisfy your condition. If I were you, I'd look at the first nontrivial case, which would be a complex $4$-manifold and with $p=2$, and see whether I could say anything interesting in that case. | |
| Dec 25, 2011 at 15:03 | history | edited | Robert Bryant | CC BY-SA 3.0 |
fixed grammar and improved formatting
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| Dec 25, 2011 at 5:06 | comment | added | y2011 | Sorry Bryant: $\phi$ should be $\sigma$. | |
| Dec 25, 2011 at 5:03 | history | edited | y2011 | CC BY-SA 3.0 |
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| Dec 24, 2011 at 23:44 | comment | added | Robert Bryant | @diverietti: I'm guessing that the description of the problem is somewhat mangled, which is why I asked about $\phi$. I suspect that y2011 probably wanted to put some condition on $\sigma$ beyond just being a real $(p,p)$-form. For example, y2011 might want it to be positive (or at least non-negative) on complex $p$-planes. Some kind of inequality such as that might give one access to area bounds for complex submanifolds of $X$, which y2011 could then use in the same way that Gromov used the taming condition to get compactness for the moduli space of curves (i.e., the $p=1$ case). | |
| Dec 24, 2011 at 14:06 | comment | added | diverietti | what about $\sigma=-\omega^p$? | |
| Dec 24, 2011 at 12:59 | comment | added | Robert Bryant | What is $\phi$, and what does it have to do with anything? | |
| Dec 24, 2011 at 9:10 | comment | added | Gunnar Þór Magnússon | Where does this notion come from? | |
| Dec 24, 2011 at 7:44 | history | edited | y2011 | CC BY-SA 3.0 |
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| Dec 24, 2011 at 7:36 | history | edited | y2011 | CC BY-SA 3.0 |
added 2 characters in body; added 2 characters in body; edited title
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| Dec 24, 2011 at 7:14 | history | asked | y2011 | CC BY-SA 3.0 |